Mine the Gap for Mathematical Understanding, Grades 6-8: Common Holes and Misconceptions and What To Do About Them (Corwin Mathematics Series)

See a gap in understanding? Mine it to move your students forward. How good are you at exploiting students’ mathematical mistakes? In this remarkable book, the authors remind us that student mistakes are not random, and when we take the time to "mine the gap," we can dispel misunderstandings before they take root. Included are 180 downloadable high-quality tasks, aligned to the standards and big ideas of grades 6–8 mathematics. Each task includes sample student work, commentary on strengths and gaps, and next instructional steps. Whether you use this bank of tasks for instruction or assessment, you will love how it helps you easily identify students’ thinking and then follow up with instruction that brings clear, complete understanding. Cover The Book at a Glance Contents Big Ideas and Tasks at a Glance Acknowledgments About the Authors Introduction Chapter 1. Rich Mathematics Tasks, Student Misconceptions, Using Tasks Chapter 2. Number Systems Big Idea 1. Addition and Subtraction of Fractions Big Idea 2. Multiplication and Division of Fractions Big Idea 3. Reasoning About Addition and Subtraction of Fractions Big Idea 4. Reasoning About Multiplication and Division of Fractions Big Idea 5. Problem Solving With Fractions Big Idea 6. Decimals as Numbers Big Idea 7. Addition and Subtraction With Decimals Big Idea 8. Multiplication and Division With Decimals Chapter 3. Integers Big Idea 9. Representing Integers Big Idea 10. Representing Integers on Number Lines Big Idea 11. More Representing Integers on Number Lines Big Idea 12. Comparing Integers Big Idea 13. Addition With Integers Big Idea 14. Subtraction With Integers Big Idea 15. Multiplication With Integers Big Idea 16. Division With Integers Chapter 4. Ratio, Proportion, and Percent Big Idea 17. Representing Ratios Big Idea 18. Equivalent Ratios Big Idea 19. Unit Rates Big Idea 20. Using Ratios to Solve Problems Big Idea 21. Reasoning With Percents Big Idea 22. Unit Rate as Slope Chapter 5. Expressions, Equations, and Functions Big Idea 23. Writing Expressions Big Idea 24. Evaluating Expressions Big Idea 25. Equivalent Expressions Big Idea 26. Writing Equations Big Idea 27. Solving Equations Big Idea 28. Inequalities Big Idea 29. Function Tables Big Idea 30. Reasoning About Graphing Big Idea 31. Comparing Functions Big Idea 32. Systems of Equations Chapter 6. Geometry Big Idea 33. Area of Composite Figures Big Idea 34. Nets and Three-Dimensional Figures Big Idea 35. Surface Area and Volume Big Idea 36. Volume of Cylinders and Cones Big Idea 37. Angle Relationships Big Idea 38. Transformations, Similarity, and Congruence Big Idea 39. Distance and the Pythagorean Theorem Chapter 7. Statistics Big Idea 40. Univariate Categorical Data Big Idea 41. Univariate Quantitative Data Big Idea 42. Displays of Univariate Quantitative Data Big Idea 43. Deviations From the Mean Big Idea 44. Bivariate Categorical Data Big Idea 45. Bivariate Quantitative Data Chapter 8. What Do We Do Next? References and Additional Resources Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students'responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni and Jennifer Rose Novak help us value our students'misconceptions and incomplete understandings as much as their correct ones—because it's the gap in their understanding today that holds the secrets to planning tomorrow's best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6–8 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task four student examples of the completed task showcasing a distinct'gap'commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks It's time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students'reasoning, better at discerning the quality and clarity of students'understanding, and better at planning teaching based on the gaps you see. "How good are you at exploiting students mathematical mistakes? In this remarkable book, the authors remind us that student mistakes are not random, and when we take the time to "mine the gap," we can dispel misunderstandings before they take root. Included are 180 downloadable high-quality tasks, aligned to the standards and big ideas of grades 68 mathematics. Each task includes sample student work, commentary on strengths and gaps, and next instructional steps. Whether you use this bank of tasks for instruction or assessment, you will love how it helps you easily identify students thinking and then follow up with instruction that brings clear, complete understanding." -- Amazon.com Discover the "why" behind students' math mistakes with this bank of 180 downloadable, standards-aligned math tasks, common misunderstandings, and next instructional steps.